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Introduction to Electrical & Computer Engineering Digital Circuits – Very Brief Introduction Dr. Cynthia Furse University of Utah 1 Digital Circuits – Brief Intro • • • • Analog & Digital Binary (Digital) Numbers & Binary Math Computers & Binary Digital Logic Gates NOT OR XOR AND NAND • Hooking up Digital Circuits 2 Digital vs. Analog • Digital is fixed (can take one or a few values, something you can count) • Analog varies (can take any value, something you can measure) 3 Analog vs. Digital – Fuel Gauge • Analog Gauge tells you ‘how much’ fuel you have • Digital Light tells you you have enough (off) or you don’t (on) 4 Analog vs. Digital – Clocks • Analog Clock tells you ‘what time it is’ (continuous) • Digital clock tells you what hour and minute it is (countable) 5 Dr. Thomas Stockham University of Utah • Analog opera recordings have distortion • Digital Recording lets you remove distortion 6 Analog vs. Digital – Voltmeters • Analog Voltmeter tells you ‘what voltage it is’ (continuous) • Digital voltmeter tells you voltage to xx.xx digits (countable) • OR just ‘on’ and ‘off’ 7 Analog vs. Digital – Voltages • Analog Voltage can be ‘any value’ (Dimmer Switch) • Digital voltage is a limited set of voltages On =1 OR Off = 0 8 Analog vs. Digital – Voltages • Analog Voltage can be ‘any value’ • Digital voltage is a limited set of voltages (Stairstepped) 9 Digital Digital – Represent with Binary #s 10 Analog to Digital Conversion (ADC) Digital to Analog Conversion (DAC) • Analog Voltage can be ‘any value’ • Digital voltage is a limited set of voltages – Quantization Error 11 Counting with Binary #s • • • • • • • • 000 = 0 001 = 1 010 = 2 011 = 3 100 = 4 101 = 5 110 = 6 111 = 7 12 Bits & Bytes • 0000 0000 << 8 BITS = 1 Byte 13 Computer Numbers Computers represent numbers as a set of bits (8,16,32 bit) & an exponent 2000 = 2 x 10^3 00000010 = 2 00000011 = 3 14 Computers Represent Letters with ASCII codes • • • • • A = 0100 0001 = ‘41’ B = 0100 0010 = ‘42’ C = 0100 0011 = ‘43’ D = 0100 0100 = ‘44’ Etc. a = 0110 0001 = ‘61’ b = 0110 0010 = ‘62’ c = 0110 0011 = ‘63’ d = 0110 0100 = ‘64’ 15 Write your name in ASCII A B C D E F G H 00000001 00000010 00000011 00000100 00000101 00000110 00000111 00001000 I J K L M N O P Q 00001001 00001010 00001011 00001100 00001101 00001110 00001111 00010000 00010001 R S T U V W X Y Z 00010010 00010011 00010100 00010101 00010110 00010111 00011001 00011010 00011010 16 How Computers Represent Pictures Pixel (eg. DPI = Dots per inch) • Digital (pixels) Analog (? Or just more pixels) 17 How Computers Represent Pictures Color: Red + Green + Blue (RGB) • Wikipedia 18 Computer Logic: • 5V = ‘1’ = ‘on’ = ‘yes’ = ‘true’ • 0V = ‘0’ = ‘Off’ = ‘no’ = ‘false’ 19 Example: Battery Voltage Sensing • A battery is considered low when its voltage is under 1.3V • Battery 1 Battery 2 20 Example: Is the Battery Charged? • ECE-speak: Is the battery voltage above 1.3V? – Convert voltage to digital (0 or 5) =5V Battery voltage Vb = A(Vb-1.3V) 1.3V 0V =5V = ‘1’ 0V = ‘0’ 21 Example: Are BOTH Batteries Charged? • Are Vo1 AND Vo2 both ‘1’? AND Vo1=IN A 0 0 1 1 Vo1=IN B 0 1 0 1 OUT 0 0 0 1 Example: Is at least one of the Batteries Charged? • Is either Vo1 OR Vo2 ‘1’? OR Vo1=IN A 0 0 1 1 Vo2=IN B 0 1 0 1 OUT 0 1 1 1 Example: Does at least one of the batteries need to be charged? • Is at least one of Vo1 AND Vo2 ‘0’? NAND IN A 0 0 1 1 IN B 0 1 0 1 OUT 1 1 1 0 Others NOT IN 0 1 OUT 1 0 Excusive-OR (XOR) Building with Logic Gates AND GND Remember the Power Supply Voltages! 5V Digital Circuits – Brief Intro • • • • Analog & Digital Binary (Digital) Numbers & Binary Math Computers & Digital Digital Logic Gates NOT OR XOR AND NAND • Hooking up Digital Circuits 27 Tombstone Rock near Moab, Utah 28